Superfluid Transition and Specific Heat of the 2D x-y Model: Monte Carlo Simulation
2021
Phong H. Nguyen | Massimo Boninsegni
We present results of large-scale Monte Carlo simulations of the 2D classical x-y model on the square lattice. We obtain high accuracy results for the superfluid fraction and for the specific heat as a function of temperature, for systems of size <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>×</mo><mi>L</mi></mrow></semantics></math></inline-formula> with L up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mn>12</mn></msup></semantics></math></inline-formula>. Our estimate for the superfluid transition temperature is consistent with those furnished in all previous studies. The specific heat displays a well-defined peak, whose shape and position are independent of the size of the lattice for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>></mo><msup><mn>2</mn><mn>8</mn></msup></mrow></semantics></math></inline-formula>, within the statistical uncertainties of our calculations. The implications of these results on the interpretation of experiments on adsorbed thin films of <sup>4</sup>He are discussed.
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